6. \(\mathbf { X } = \left( \begin{array} { l l } 1 & a
3 & 2 \end{array} \right)\), where \(a\) is a constant.
- Find the value of \(a\) for which the matrix \(\mathbf { X }\) is singular.
$$\mathbf { Y } = \left( \begin{array} { r r }
1 & - 1
3 & 2
\end{array} \right)$$ - Find \(\mathbf { Y } ^ { - 1 }\).
The transformation represented by \(\mathbf { Y }\) maps the point \(A\) onto the point \(B\).
Given that \(B\) has coordinates ( \(1 - \lambda , 7 \lambda - 2\) ), where \(\lambda\) is a constant, - find, in terms of \(\lambda\), the coordinates of point \(A\).